DLOGTIME

In computational complexity theory, DLOGTIME is the complexity class of all computational problems solvable in a logarithmic amount of computation time on a deterministic Turing machine. It must be defined on a random-access Turing machine, since otherwise the input tape is longer than the range of cells that can be accessed by the machine. It is a very weak model of time complexity: no random-access Turing machine with a smaller deterministic time bound can access the whole input.^[1]

DLOGTIME-uniformity is important in circuit complexity.^[1]^[2]

References

1 2 Johnson, David S. (1990), "A catalog of complexity classes", Handbook of theoretical computer science, Vol. A, Elsevier, Amsterdam, pp. 67–161, MR 1127168 . See in particular p. 140.
↑ Allender, Eric; Gore, Vivek (1993), "On strong separations from AC⁰", Advances in computational complexity theory (New Brunswick, NJ, 1990), DIMACS Ser. Discrete Math. Theoret. Comput. Sci. 13, Amer. Math. Soc., Providence, RI, pp. 21–37, MR 1255326 . See in particular p. 23.

Important complexity classes (more)

Considered feasible	DLOGTIME AC⁰ ACC⁰ TC⁰ L SL RL NL NC SC CC P P-complete ZPP RP BPP BQP APX

Suspected infeasible	UP NP NP-complete NP-hard co-NP co-NP-complete AM QMA PH ⊕P PP #P #P-complete IP PSPACE PSPACE-complete

Considered infeasible	EXPTIME NEXPTIME EXPSPACE ELEMENTARY PR R RE ALL

Class hierarchies	Polynomial hierarchy Exponential hierarchy Grzegorczyk hierarchy Arithmetical hierarchy Boolean hierarchy

Families of classes	DTIME NTIME DSPACE NSPACE Probabilistically checkable proof Interactive proof system

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